Statistics.Sample:$swelfordMean from math-functions-0.1.5.2

Percentage Accurate: 100.0% → 100.0%

Time: 4.4s

Alternatives: 6

Speedup: 1.0×

• 20.7% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ x + \frac{y - x}{z} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ x (/ (- y x) z)))

C

double code(double x, double y, double z) {
	return x + ((y - x) / z);
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x + ((y - x) / z)
end function

Java

public static double code(double x, double y, double z) {
	return x + ((y - x) / z);
}

Python

def code(x, y, z):
	return x + ((y - x) / z)

Julia

function code(x, y, z)
	return Float64(x + Float64(Float64(y - x) / z))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + ((y - x) / z);
end

Wolfram

code[x_, y_, z_] := N[(x + N[(N[(y - x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]

Initial Program: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + \frac{y - x}{z} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ x (/ (- y x) z)))

C

double code(double x, double y, double z) {
	return x + ((y - x) / z);
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x + ((y - x) / z)
end function

Java

public static double code(double x, double y, double z) {
	return x + ((y - x) / z);
}

Python

def code(x, y, z):
	return x + ((y - x) / z)

Julia

function code(x, y, z)
	return Float64(x + Float64(Float64(y - x) / z))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + ((y - x) / z);
end

Wolfram

code[x_, y_, z_] := N[(x + N[(N[(y - x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]

Alternative 1: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + \frac{y - x}{z} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ x (/ (- y x) z)))

C

double code(double x, double y, double z) {
	return x + ((y - x) / z);
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x + ((y - x) / z)
end function

Java

public static double code(double x, double y, double z) {
	return x + ((y - x) / z);
}

Python

def code(x, y, z):
	return x + ((y - x) / z)

Julia

function code(x, y, z)
	return Float64(x + Float64(Float64(y - x) / z))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + ((y - x) / z);
end

Wolfram

code[x_, y_, z_] := N[(x + N[(N[(y - x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 2: 61.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{-x}{z}\\ \mathbf{if}\;z \leq -2200000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{-60}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-232}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{-280}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-9}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (- x) z)))
   (if (<= z -2200000000000.0)
     x
     (if (<= z -1.25e-60)
       (/ y z)
       (if (<= z -2.3e-232)
         t_0
         (if (<= z 4.3e-280) (/ y z) (if (<= z 1.3e-9) t_0 x)))))))

C

double code(double x, double y, double z) {
	double t_0 = -x / z;
	double tmp;
	if (z <= -2200000000000.0) {
		tmp = x;
	} else if (z <= -1.25e-60) {
		tmp = y / z;
	} else if (z <= -2.3e-232) {
		tmp = t_0;
	} else if (z <= 4.3e-280) {
		tmp = y / z;
	} else if (z <= 1.3e-9) {
		tmp = t_0;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = -x / z
    if (z <= (-2200000000000.0d0)) then
        tmp = x
    else if (z <= (-1.25d-60)) then
        tmp = y / z
    else if (z <= (-2.3d-232)) then
        tmp = t_0
    else if (z <= 4.3d-280) then
        tmp = y / z
    else if (z <= 1.3d-9) then
        tmp = t_0
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = -x / z;
	double tmp;
	if (z <= -2200000000000.0) {
		tmp = x;
	} else if (z <= -1.25e-60) {
		tmp = y / z;
	} else if (z <= -2.3e-232) {
		tmp = t_0;
	} else if (z <= 4.3e-280) {
		tmp = y / z;
	} else if (z <= 1.3e-9) {
		tmp = t_0;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -x / z
	tmp = 0
	if z <= -2200000000000.0:
		tmp = x
	elif z <= -1.25e-60:
		tmp = y / z
	elif z <= -2.3e-232:
		tmp = t_0
	elif z <= 4.3e-280:
		tmp = y / z
	elif z <= 1.3e-9:
		tmp = t_0
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(-x) / z)
	tmp = 0.0
	if (z <= -2200000000000.0)
		tmp = x;
	elseif (z <= -1.25e-60)
		tmp = Float64(y / z);
	elseif (z <= -2.3e-232)
		tmp = t_0;
	elseif (z <= 4.3e-280)
		tmp = Float64(y / z);
	elseif (z <= 1.3e-9)
		tmp = t_0;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -x / z;
	tmp = 0.0;
	if (z <= -2200000000000.0)
		tmp = x;
	elseif (z <= -1.25e-60)
		tmp = y / z;
	elseif (z <= -2.3e-232)
		tmp = t_0;
	elseif (z <= 4.3e-280)
		tmp = y / z;
	elseif (z <= 1.3e-9)
		tmp = t_0;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[((-x) / z), $MachinePrecision]}, If[LessEqual[z, -2200000000000.0], x, If[LessEqual[z, -1.25e-60], N[(y / z), $MachinePrecision], If[LessEqual[z, -2.3e-232], t$95$0, If[LessEqual[z, 4.3e-280], N[(y / z), $MachinePrecision], If[LessEqual[z, 1.3e-9], t$95$0, x]]]]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 3: 72.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.05 \cdot 10^{+25} \lor \neg \left(x \leq -4.8 \cdot 10^{-92} \lor \neg \left(x \leq -3.3 \cdot 10^{-144}\right) \land x \leq 2.7 \cdot 10^{-95}\right):\\ \;\;\;\;x - \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.05e+25)
         (not
          (or (<= x -4.8e-92) (and (not (<= x -3.3e-144)) (<= x 2.7e-95)))))
   (- x (/ x z))
   (/ y z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.05e+25) || !((x <= -4.8e-92) || (!(x <= -3.3e-144) && (x <= 2.7e-95)))) {
		tmp = x - (x / z);
	} else {
		tmp = y / z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-1.05d+25)) .or. (.not. (x <= (-4.8d-92)) .or. (.not. (x <= (-3.3d-144))) .and. (x <= 2.7d-95))) then
        tmp = x - (x / z)
    else
        tmp = y / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.05e+25) || !((x <= -4.8e-92) || (!(x <= -3.3e-144) && (x <= 2.7e-95)))) {
		tmp = x - (x / z);
	} else {
		tmp = y / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.05e+25) or not ((x <= -4.8e-92) or (not (x <= -3.3e-144) and (x <= 2.7e-95))):
		tmp = x - (x / z)
	else:
		tmp = y / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.05e+25) || !((x <= -4.8e-92) || (!(x <= -3.3e-144) && (x <= 2.7e-95))))
		tmp = Float64(x - Float64(x / z));
	else
		tmp = Float64(y / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -1.05e+25) || ~(((x <= -4.8e-92) || (~((x <= -3.3e-144)) && (x <= 2.7e-95)))))
		tmp = x - (x / z);
	else
		tmp = y / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.05e+25], N[Not[Or[LessEqual[x, -4.8e-92], And[N[Not[LessEqual[x, -3.3e-144]], $MachinePrecision], LessEqual[x, 2.7e-95]]]], $MachinePrecision]], N[(x - N[(x / z), $MachinePrecision]), $MachinePrecision], N[(y / z), $MachinePrecision]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 4: 85.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.9 \cdot 10^{-5} \lor \neg \left(z \leq 2.1 \cdot 10^{-5}\right):\\ \;\;\;\;x - \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -4.9e-5) (not (<= z 2.1e-5))) (- x (/ x z)) (/ (- y x) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -4.9e-5) || !(z <= 2.1e-5)) {
		tmp = x - (x / z);
	} else {
		tmp = (y - x) / z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-4.9d-5)) .or. (.not. (z <= 2.1d-5))) then
        tmp = x - (x / z)
    else
        tmp = (y - x) / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -4.9e-5) || !(z <= 2.1e-5)) {
		tmp = x - (x / z);
	} else {
		tmp = (y - x) / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -4.9e-5) or not (z <= 2.1e-5):
		tmp = x - (x / z)
	else:
		tmp = (y - x) / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -4.9e-5) || !(z <= 2.1e-5))
		tmp = Float64(x - Float64(x / z));
	else
		tmp = Float64(Float64(y - x) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -4.9e-5) || ~((z <= 2.1e-5)))
		tmp = x - (x / z);
	else
		tmp = (y - x) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -4.9e-5], N[Not[LessEqual[z, 2.1e-5]], $MachinePrecision]], N[(x - N[(x / z), $MachinePrecision]), $MachinePrecision], N[(N[(y - x), $MachinePrecision] / z), $MachinePrecision]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 5: 62.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -72000000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{+16}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -72000000000000.0) x (if (<= z 1.75e+16) (/ y z) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -72000000000000.0) {
		tmp = x;
	} else if (z <= 1.75e+16) {
		tmp = y / z;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-72000000000000.0d0)) then
        tmp = x
    else if (z <= 1.75d+16) then
        tmp = y / z
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -72000000000000.0) {
		tmp = x;
	} else if (z <= 1.75e+16) {
		tmp = y / z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -72000000000000.0:
		tmp = x
	elif z <= 1.75e+16:
		tmp = y / z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -72000000000000.0)
		tmp = x;
	elseif (z <= 1.75e+16)
		tmp = Float64(y / z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -72000000000000.0)
		tmp = x;
	elseif (z <= 1.75e+16)
		tmp = y / z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -72000000000000.0], x, If[LessEqual[z, 1.75e+16], N[(y / z), $MachinePrecision], x]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 6: 36.6% accurate, 7.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 x)

C

double code(double x, double y, double z) {
	return x;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x
end function

Java

public static double code(double x, double y, double z) {
	return x;
}

Python

def code(x, y, z):
	return x

Julia

function code(x, y, z)
	return x
end

MATLAB

function tmp = code(x, y, z)
	tmp = x;
end

Wolfram

code[x_, y_, z_] := x

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Reproduce

herbie shell --seed 2023343 
(FPCore (x y z)
  :name "Statistics.Sample:$swelfordMean from math-functions-0.1.5.2"
  :precision binary64
  (+ x (/ (- y x) z)))